An Etymological Dictionary of Astronomy and Astrophysics

فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory



Number of Results: 14 Search : integral
definite integral
  درستال ِ هدارمند   
dorostâl-e hedârmand

Fr.: intégrale définie   

An integral with upper and lower limits.

definite; → integral.

differential and integral calculus
  افماریک ِ دگرسانه‌ای و درستالی   
afmârik-e degarsâne-yi va dorostâli

Fr.: calcul différentiel et intégral   

The two branches of mathematics that make up the → calculus. → differential calculus; → integral calculus.

differential; → integral; → calculus.

double integral
  درستال ِ دوتایی   
dorostâl-e dotâyi

Fr.: intégrale double   

The simplest case of a → multiple integral.

double; → integral.

Fourier integral
  درستال ِ فوریه   
dorostâl-e Fourier

Fr.: intégrale de Fourier   

An integral used in the → Fourier transform.

Fourier analysis; → integral.

Fresnel integrals
  درستال‌های ِ فرنل   
dorostâlhâ-ye Fresnel

Fr.: intégrales de Fresnel   

Two integrals that involve quadratic equations in the sine and cosine functions and are defined as: C(x) = ∫ cos (πt2/2) dt and C(y) = ∫ sin (πt2/2) dt, integrated from 0 to x. They are quite frequently used in optics studying → Fresnel diffraction and similar topics. The Fresnel integrals are also used in railway and freeway constructions. These integrals may be evaluated to arbitrary precision using → power series. Alternatively the amplitudes may be found graphically by use of → Cornu's spiral.

Fresnel diffraction; → integral.

indefinite integral
  دُرُستال ِ ناهدارمند   
dorostâl-e nâhedârmand

Fr.: intégrale indéfinie   

Math.: An integral without upper and lower limits. The general antiderivative of a function. → definite integral.

definite; → integral.

  ۱) درست؛ ۲) دُرُستال   
1) dorost; 2) dorostâl

Fr.: 1) intégral; 2) intégrale   

1) Consisting of whole numbers or integers.
2) Mathematical function obtained by the process of → integration.

Integral, from M.Fr. intégral, from M.L. integralis "forming a whole," → integer "whole."

1) Dorostâl, from dorost "whole, complete; healthy; right," related to dorud "benediction, praise, thanksgiving," from Mid.Pers. drust "whole; healthy; well, right," drôd "health, thriving;" O.Pers. duruva- "firm, certain, immune;" Av. druua- "healthy;" cf. Skt. dhruvá- "fixed, firm, immovable, lasting, certain;" Russ. zdorovyjj "healthy;" See also → sound.
2) Dorostâl, from dorost + -âl, → -al.

integral calculus
  افماریک ِ دُرُستالی   
afmârik-e dorostâli

Fr.: calcul intégral   

Branch of the calculus that deals with integration and its use in finding volumes, areas, equations of curves, solutions of differential equations, etc.

integral; → calculus.

integral equation
  هموگش ِ دُرُستالی   
hamugeš-e dorostâli

Fr.: équation intégrale   

An equation involving an unknown function that appears as part of an integrand.

integral; → equation.

integral field spectroscopy
  بیناب‌نمایی ِ درست ِ میدان   
binâbnemâyi-ye dorost-e meydân

Fr.: spectroscopie intégrale de champ   

A technique in spectroscopy for recording a spectrum from each point of an extended object. The field of view image is divided into a multitude of small components using different methods, e.g. lenslet arrays, fiber bundles, or image slicers. From each component a spectrum is extracted or an image is reconstructed at a particular wavelength.

integral; → field; → spectroscopy.

integral function
  کریای ِ دُرُستالی   
karyâ-ye dorostâli

Fr.: fonction intégrale   

A function whose image is a subset of the integers, i.e. that takes only integer values.

integral; → function.

integral operator
  آپارگر ِ دُرُستالی   
âpârgar-e dorostâli

Fr.: opérateur intégral   

Math.: An operator whose inverse is a differential operator.

integral; → operator.

Jacobi integral
  درستال ِ یاکوبی   
dorostâl-e Jacobi

Fr.: intégrale de Jacobi   

The integral admitted by the equations of a body of infinitesimal mass moving under the → gravitational attractions of two massive bodies, which move in circles about their → center of gravity. The Jacobi integral is the only known conserved quantity for the circular → restricted three-body problem. In the co-rotating system it is expressed by the equation: (1/2) (x·2 + y·2 + z·2) = U - CJ, where the dotted coordinates represent velocities, U is potential energy, and CJ the constant of integration (→ zero-velocity surface). The Jacobi integral has been used for two different purposes: 1) to construct surfaces of zero velocity which limit the regions of space in which the small body, under given initial conditions, can move, and 2) to derive a criterion (→ Tisserand's parameter) for re-identification of a → comet whose orbit has suffered severe perturbations by a planet. Also known as Jacobi constant.

Named after Karl Gustav Jacobi (1804-1851), a German mathematician who did important work on elliptic functions, partial differential equations, and mechanics; → integral.

multiple integral
  درستال ِ بستایی   
dorostâl-e bastâyi

Fr.: intégrale multiple   

A series of successive integrations in which the integral operator acts on the result of preceding integration.

multiple; → integral.